Nonlinear response and stability analysis of beams using finite elements in time

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Abstract
The dynamic response and stability analysis of beams undergoing large deflections and rotations is analyzed using the finite-element method in time. This formulation provides an efficient and consistent approach to predicting the dynamic response of nonlinear periodic systems as well as their stability boundaries based on Floquet's theory. This paper has two goals to present the formulation of the finite element in time equations for naturally curved and twisted beams undergoing large deflections and rotations, and to discuss the predictions of this method when applied to several classical nonlinear beam problems for which analytical solutions exist and, in some cases, experimental results are available. In all cases, close agreement is found between the analytical results and the predictions of the finite element in time approach, which appears to be an efficient and reliable technique for nonlinear dynamic response and stability analysis of periodic systems

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